Working Paper Series 

Congressional Budget Office 

Washington, D.C. 

Assessing the Relationship between Economic Stability and 

Dynamic Employment Responses to Aggregate Shocks 

Naomi N. Griffin 

Congressional Budget Office 

Washington, D.C. 

E-mail: naomi.griffin@cbo.gov 

March 2007 

2007-04 

Working papers in this series are preliminary and are circulated to stimulate discussion 

and critical comment. These papers are not subject to CBO's formal review and editing 

processes. The analysis and conclusions expressed in them are those of the authors and 

should not be interpreted as those of the Congressional Budget Office. References in 

publications should be cleared with the authors. Papers in this series can be obtained at 

www.cbo.gov (select Publications, and then select Working and Technical Papers). 
 1

Abstract 

Previous studies have identified a significant drop in the volatility of the U.S. GDP and 

other measures of aggregate activity since the mid-1980s. Yet uncertainty remains as to 

whether the reduced size and frequency of macroeconomic shocks, or the economy’s 

reduced responses to shocks, are producing aggregate economic stability. To investigate 

this issue, this paper looks at the changes in aggregate employment responses to shocks. 

Using an interrelated factor demand model, this paper finds that the monthly employment 

elasticity to unanticipated demand shocks has declined by more than 80% in the 

manufacturing industry since 1984 in comparison with the elasticity during prior decades. 

Similarly, the work-hour elasticity to unanticipated demand shocks declined by more than 

60%. At the same time, the paper does not find any observable change in the pattern of 

inventory adjustment, except in its responses to future demand. Using vector 

autoregressions (VARs), the paper also finds that the dynamic responses of employment 

to some measures of aggregate economic shocks, such as oil shocks and monetary policy 

shocks, are smaller and less volatile since 1984. This result holds for both manufacturing 

at monthly frequency and aggregate employment series at monthly and quarterly 

frequencies. 
 2

Table of Contents 

1. INTRODUCTION........................................................................................................ 3

2. INTERRELATED FACTOR DEMAND MODEL................................................... 8

MODEL.........................................................................................................................................8

DATA AND RESULTS ..................................................................................................................11

3. VAR ANALYSIS........................................................................................................ 17

VAR SPECIFICATIONS................................................................................................................17

DATA AND RESULTS ..................................................................................................................19

4. CONCLUSION........................................................................................................... 25

REFERENCES................................................................................................................ 28

FIGURES AND TABLES............................................................................................... 31
 3

1. Introduction 

 Over the past 20 years, the volatility of U.S. real GDP growth and other 

macroeconomic variables has been far milder than in preceding decades. The reduction 

in volatility, in turn, has reduced the frequency, length, and magnitude of recessions. 

While many economists have recognized this change, there is no consensus regarding the 

causes of this newfound macroeconomic stability (often called the “great moderation”). 

In particular, whether the stability arises from a reduction in the volatility of shock 

processes or from reduced responses to shocks via a structural change in the economy is 

unclear. 

 To investigate this issue, this paper focuses on aggregate employment responses 

to shocks. If the reduction in volatility is caused entirely by fewer and smaller 

macroeconomic shocks without any changes in adjustment mechanism, employment 

responses to macroeconomic shocks should remain unchanged. If, however, structural 

change is partly responsible for the reduced volatility in macroeconomic variables, the 

employment response to these shocks should be affected and should be smaller over the 

past 20 years.1

 Accordingly, an evaluation of the dynamic employment responses to 

various disturbances to the economy allows us to see if the economy has become more 

resilient as a result of structural changes. 

 

1

 Note that these two causes are not necessarily distinct concepts. For example, changes in macroeconomic 

shock processes (i.e., reduced variance or persistence) may trigger a different pattern of production 

adjustment. Ramey and Vine (2006) show the reduced persistence of sales shocks can lower employment 

volatility, as producers use work-hour and inventory adjustment more intensively relative to employment to 

meet temporary fluctuations in demand. In this paper, I make a simple distinction by assuming that any 

systematic changes in employment, work-hour, or inventory adjustment mechanism are structural 

regardless of how they may be triggered by the changes in shock processes. The investigation into how 

they may be related will be left for the future. 
 4

 This exercise has important implications for policymakers, who need to determine 

appropriate policy responses when aggregate shocks hit the economy. Monetary and 

fiscal policies are often used to smooth out fluctuations in economic activity and to 

alleviate the negative impact of recessions. The effectiveness of the policies often 

depends on the timing of their implementation, which in turn depends on policymakers’ 

understanding of how the economy may handle unfavorable macroeconomic shocks. 

 This paper finds that employment and work-hour responses to shocks have been 

smaller over the last 20 years than those from the 1960s through the mid-1980s. The 

elasticity of monthly employment and work hours with respect to an unpredicted demand 

shock fell by more than 80% and 60%, respectively, in the manufacturing industry. 

Furthermore, vector autoregression (VAR) analysis shows that the dynamic responses of 

employment growth with respect to oil price and monetary policy shocks to the economy 

are smaller and less volatile since 1984 compared to preceding decades. This result is 

robust for both manufacturing and aggregate employment series. 

 Kim and Nelson (1999) and McConnell and Parez-Quiros (2000) independently 

find a break in U.S. GDP growth rate volatility in the first quarter of 1984. Similarly, 

Stock and Watson (2002) identify the structural break in the conditional variance of fourquarter GDP growth at the second quarter of 1983, with a 67% confidence interval for the 

structural break from the fourth quarter of 1982 to the third quarter of 1985. 

Furthermore, 40% of the 168 aggregate series examined have structural breaks that fall 

between 1983 and 1985. This paper does not further scrutinize the suggested break dates. 

Although it is unlikely that a break in economic activity can be assigned to a single date, 
 5

the paper takes the date as given and focuses on the question of the causes of employment 

stability. 

 Although several explanations have emerged, substantial uncertainty remains as 

to what caused the observed reduction in aggregate volatility.2 Leading explanations 

include the “good practice” hypothesis, driven by technological innovation and inventory 

management; the “good policy” hypothesis, linking better monetary policies to 

macroeconomic outcome; the “good luck” hypothesis, which emphasizes the reduced size 

and frequency of macroeconomic shocks; and the “financial innovations” hypothesis, 

characterized by smoothed consumption, and housing and business fixed investment. 

 McConnell and Parez-Quiros (2000) and Kahn, McConnell, and Parez-Quiros 

(2002) suggest that technological innovations have helped firms to better predict and 

prepare for the changes in demand conditions and consequently reduce inventory 

volatility. Furthermore, they claim that a smaller inventory adjustment has led to a 

reduction in output volatility.3 Clarida, Gali, and Gertler (2000) argue that improved use 

of monetary policy by the Federal Reserve to control inflation contributed to the 

stabilization of aggregate output.4

 In contrast, Ahmed, Levin, and Wilson (2002) and 

Stock and Watson (2002) suggest that much of the reduction in aggregate volatility is 

 

2

 An excellent literature review is provided by Cecchetti, Flores-Lagunes, and Krause (2006). 

3

 Their theoretical explanation is tied to output inventories based on the observation that the volatility of 

output fell by more than the volatility of final sales. However, Herrera and Pesavento (2005) show that 

much of the reduction in inventory volatility arises from input inventory such as materials and supplies, 

instead of output inventory. 

4

 However, Ahmed, Levin, and Wilson (2002) and Stock and Watson (2002) argue that improved monetary 

policy alone is insufficient to explain the observed stability in output. For example, Stock and Watson 

(2002) estimate that improved monetary policy can account for 10-25% of the reduction in aggregate 

economic volatility. 
 6

caused by a reduction in the size of shocks.5 Dynan, Elmendorf, and Sichel (2006) show 

that financial innovations enhanced individuals’ ability to borrow and that this in turn 

smoothed consumption, housing and business fixed investment, and hence aggregate 

volatility. 

 This paper does not assess each of these hypotheses but instead examines 

macroeconomic stability from another angle by looking at the dynamics of employment 

responses to shocks. By doing so, it aims to shed further light on shock versus structural 

change hypotheses. The paper uses two methods for the investigation. The first is the 

interrelated factor demand model suggested by Topel (1982), which allows us to estimate 

the scope of employment elasticity to unanticipated demand shocks. Since the model 

requires shipment data and performs more robustly using monthly frequency to capture 

demand shock processes, this exercise was applied only to the manufacturing industry 

because of limitations on data availability. The second method used is vector 

autoregressions (VARs). VAR analysis allows us to capture the dynamic employment 

responses to some measures of macroeconomic disturbances. This exercise was 

performed for both the manufacturing series at a monthly frequency and the aggregate 

employment series at monthly and quarterly frequencies. Both methods indicate that 

employment sensitivity to shock variables has been smaller since 1984 than in preceding 

decades. 

 

5

 Stock and Watson (2002) discuss the reduction in monetary, fiscal, productivity, oil price, and other 

commodity price shocks. The volatility of the real oil price is higher in the post-1984 sample. 

Accordingly, their conclusion about an oil price shock is based on a Hamilton measure, which considers 

major supply disruptions as oil shocks. 
 7

 While it is beyond the scope of this paper, an important question concerns the 

theoretical underpinning of this result. One could argue that the reduced aggregate 

sensitivity of employment to shocks arises from changes in microeconomic behavior at 

the firm level. For example, greater wage flexibility at the firm level may lead to reduced 

employment sensitivity to shocks. Although validation of this hypothesis would likely 

require a firm-level data set and data on total labor compensation, simple exercises 

performed in this paper do not find an increased flexibility in aggregate hourly earnings. 

Another possible explanation relates to labor adjustment costs: higher costs can reduce 

firms’ employment responses to shocks. Similarly, nonconvex adjustment costs may 

cause employment volatility to interact nonlinearly with the variance of shocks.6

 Further 

empirical investigations of these possibilities would require firm-level data. 

 Alternatively, one might argue that reduced aggregate employment responses to 

shocks come from greater heterogeneity in firms’ responses to shocks and the resulting 

reduction in covariance across firms’ activities. If this were the case, firm-level and 

aggregate volatility might not move in the same direction.7 Although studies have given 

conflicting evidence, the most comprehensive research using the Census Bureau’s 

Longitudinal Business Database (LBD), which covers all U.S. firms with paid 

 

6

 For instance, hiring or firing costs may prevent employers from making positive hiring or firing decisions 

for small enough shocks. 

7

 Based on the evidence of a rise in firm-level volatility among publicly traded firms, Philippon (2003) 

suggests a model in which greater competition generates higher firm-level volatility while price flexibility 

reduces aggregate volatility. Comin and Mulani (2005) conjecture that an increased investment in firmspecific R&D combined with a reduced investment in common technology can explain higher firm-level 

volatility and lower aggregate volatility. 
 8

employees, shows that average firm-level volatility, in terms of the employment growth 

rate, declined between 1978 and 2001.8 

 This paper proceeds as follows. Section 2 provides a description of the 

interrelated factor demand model and discusses the results, which characterize 

employment, work hours, and inventory responses to unpredicted and predicted demand 

shocks. Section 3 provides the specifications used for VARs and the results, describing 

the changes in the dynamic employment growth responses to aggregate shocks such as oil 

price and monetary policy shocks. Section 4 concludes and identifies areas for additional 

investigation. 

2. Interrelated Factor Demand Model 

Model 

 Topel's interrelated factor demand model captures the interdependence of 

decisions regarding the optimal levels of the following three variables: employment, 

work hours, and inventories. Given the initial values of these variables, the exogenous 

shock determines the desired level of each in this model. The exogenous shock here is 

the product demand, and the model distinguishes predicted and unpredicted components 

 

8

 Studies using the database on publicly traded firms have found that firm-level volatility has increased 

while aggregate volatility has dropped. Comin and Philippon (2005) and Comin and Mulani (2006) show 

that firm-level volatility indicated by the growth rate of sales has increased over the past 50 years. 

Campbell, Lettau, Malkiel, and Xu (2001) use a capital asset pricing model (CAPM) and find that the role 

of idiosyncratic risk in explaining the total time-series volatility of stock returns has increased over the last 

couple of decades in the U.S., while market volatility has been stable over the same period. However, 

using the Longitudinal Business Database, Davis, Haltiwanger, Jarmin, and Miranda (2006) show that 

publicly held and private firms follow opposite trends in terms of employment volatility: while publicly 

traded firms exhibit a rising trend in employment volatility, privately held firms exhibit a declining trend. 

The overall volatility declines when using employment as a weight. 
 9

of product demand captured by the shipment series. More specifically, the following set 

of equations is used to investigate the interrelated factor demand decision rules: 

 10 11 1 12 1 13 1 1 1

0

,

T u Lt t tt t L H I q q trend season t s τ τ

τ

αα α α β λ − −− +

=

=+ + + + + + + ∑ (1) 

 20 21 1 22 1 23 1 2 2

0

,

T u Ht t tt t L H I q q trend season t s τ τ

τ

αα α α β λ − −− +

=

=+ + + + + + + ∑ (2) 

 30 31 1 32 1 33 1 3 3

0

.

T u

t t tt t t I L H I q q trend seasons τ τ

τ

αα α α β λ − −− +

=

=+ + + + + + + ∑ (3) 

Lt , Ht , and t I refer to employment, work hours, and inventory in natural 

logarithms at time t . T is the planning horizon, 

t q is the predicted component of 

demand while u

t q captures the unpredicted component (i.e.,  t t q q − ), and α , β , and λ

are the impact elasticity coefficients to be estimated. Each regression includes a trend 

variable and seasonal dummies. 

 The following propositions are given by Topel: first, the speed-of-adjustment 

parameter (α jj where j=1, 2, or 3) is expected to increase (i.e., adjustment slows) as the 

labor adjustment costs increase or inventory costs decrease. These parameter values 

equal zero when inputs are freely variable and unity when they are fixed. Second, 

employment and work hours should respond positively to a rise in current unpredicted 

shocks while inventories should respond negatively. Responses of employment and work 

hours to current predicted demand are less certain as there may be smoothing incentives. 

A lower cost of inventories as well as higher labor adjustment costs increase both 

inventory and work-hour responses to current predicted or unpredicted shocks, whereas 
 10

they reduce the employment responses to those shocks. Third, a rise in future expected 

shipments ( 

0

T

t q ∑τ τ = + ) should increase the demand for employment, work hours, and 

inventories.9 

 Next, it is assumed that expected monthly demand values depend only on the past 

values of shipments and not on the other endogenous variables. More specifically, the 

demand condition, characterized by the monthly series on log shipments, t q , follows a 

seasonally differenced autoregressive integrated moving average (ARIMA) process of the 

following form: 

12 12 ( )(1 )(1 ) (1 ) ( ) Aa L L Lq LML t m t − − =−δ u (4) 

where L represents a lag operator, ( ) Aa L and ( ) Mm L are polynomials of orders a and 

m respectively in the lag operator,δ is a seasonal moving average parameter, and t u is 

the white noise error term. 

 Following Topel (1982), an additional structure is imposed on the lead 

distributions of β jτ . Namely, I assume that they follow a third-order Almon polynomial, 

requiring the shortest planning horizon to be 4 months. I set the baseline planning 

horizon to 9 months, although assumed planning horizons of 6 or 12 months produce the 

same main results. 

 

9

 The expected τ-period ahead shipment at time t is given by  1, 2, | ... t t tt q Eq u u +τ + −− τ = ⎡ ⎤ ⎣ ⎦. 
 11

Data and Results 

 Estimation based on the interrelated factor demand model uses monthly 

seasonally unadjusted series on shipments, employment, work hours, and inventories in 

the manufacturing industry from January 1958 through December 2005.10 The data on 

shipments and inventories come from Current Industrial Reports published by the 

Census Bureau. Finished goods inventory series are used to investigate inventory 

adjustment, as other types of inventories such as materials and supplies or work-inprogress inventories are less effective substitutes for employment and work hours in 

response to demand shocks. Nonetheless, each regression includes lagged values of these 

inventories to control for other relevant input factors affecting the dynamics of 

employment, work hours, and finished goods inventories.11 Nominal values of shipments 

and inventories are deflated using PPI for finished goods in the Producer Price Indexes 

provided by the Department of Labor’s Bureau of Labor Statistics (BLS). The 

employment and work-hour series come from BLS’s establishment survey.12 

 As discussed in Topel (1982), seasonally unadjusted series are preferred over 

seasonally adjusted series because “the transitory and highly predictable character of 

seasonal fluctuations makes them prime candidates for inventory smoothing and 

temporary layoffs.”13 However, as shown below, the use of seasonally adjusted data does 

 

10 The seasonally unadjusted series based on SIC classifications covers the period from January 1958 

though March 2001 (when it was discontinued), while the same series based on NAICS covers the period 

from 1992. I spliced these two seasonally unadjusted series at March 2001. 

11 The original interrelated factor demand model proposes that we include a lagged value of other input 

factors or stocks such as materials on the right-hand side of each equation. 

12 Employment is defined as “employees on nonfarm payroll” and work hour is “average weekly hours of 

production of nonsupervisory workers on private nonfarm payroll.” 

13 Footnote 16 in Topel (1982). 
 12

not change the main results; hence, it seems that much of the change comes from factors 

unrelated to seasonal adjustment. 

 Figure 1 shows shipments, employment, hours, and inventories (all in logs) from 

January 1958 to December 2005 for the manufacturing industry.14 While the volume of 

real manufacturing shipments has increased over time, the employment series does not 

exhibit any obvious trend between 1970 and 2000 and follows a steady decline after 

2001. Although all results shown cover the period after 2001, the elasticity estimates for 

the post-1984 sample are insensitive to the exclusion of data after 2001.15 

 To compare the changes in the dynamic responses to shock series, the sample 

series are split at March 1984, as most literature on aggregate volatility has identified the 

structural break in the aggregate GDP series during the first quarter of 1984. I take this 

date as given and use it for all equations, although as discussed below, Bai-Perron 

multiple structural break tests show that the suggested break date varies somewhat for 

each equation. Regardless, the main results are insensitive to the adjustment of break 

dates based on Bai-Perron tests, and will be discussed later. Finally, ordinary least 

squares (OLS) estimation of equations (1), (2), and (3) exhibits serial correlation in 

disturbance terms. Therefore, the Beach and MacKinnon maximum likelihood iterative 

procedure was used for all estimations to obtain consistent estimates of equations (1), (2), 

and (3). 

 

14 The original shipment and inventory series are in millions of dollars, and the employment figure is in 

thousands. 

15 In other words, the difference in the elasticity estimates is not driven by the factors which have caused a 

steady decline of manufacturing employment after 2001. 
 13

 Table 1 shows the estimates of an interrelated factor demand model using 

seasonally unadjusted series for the baseline case of a 9-month forecast horizon. The 

first, second, and third columns of the table show, respectively, the estimates of equations 

(1), (2), and (3). The standard errors are reported in parentheses, and the coefficients for 

future predicted demand are the sum of the coefficients for future months including the 

current month. In order to model the time-series process for demand, the best 

parsimonious specification that removed autocorrelation in the residuals was chosen 

based on the Akaike information criterion.16 Although the results are not shown here, I 

fit two separate ARIMA models for the pre- and post-1984 samples to construct a 

demand shock series.17 The standard error of the residuals (i.e., unpredicted component 

of shipments) falls by 9% during the post-1984 period, even though the standard 

deviation of the shipment series detrended by a Hodrick-Prescott filter increases by 6.5%. 

 Prior to 1984, employment responses to current unpredicted shocks were positive 

and statistically significant at the 1% level. However, the same coefficient is much 

smaller and insignificant after 1984. More specifically, the elasticity of employment with 

respect to unexpected demand shocks falls by 89%. Furthermore, these two coefficients 

are statistically different from each other. A similar change takes place for current 

predicted shocks although the elasticity estimates are smaller compared to current 

unpredicted shocks. One explanation for this result is that employment responses are 

smoothed out over time when demand shocks are predicted. Employment responses to 

 

16 I experimented with a number of specifications with both lags ranging from one to four. 

17 I used AR=4 and MA=4 for the pre-1984 period and AR=3 and MA=4 for the post-1984 period. Due to 

the lags involved in fitting the model, the pre-1984 sample series covers from June 1959 through March 

1984 and the post-1984 sample series covers from April 1984 through December 2005. 
 14

future predicted shocks are significant in both periods, but smaller after 1984. Again, 

these estimates are statistically significantly different from each other. The higher 

persistence of the employment series also highlights slower employment adjustment 

during the second period. 

 As in the employment case, the elasticity of hours with respect to current 

unpredicted shocks drops significantly and the coefficient, which drops by 66%, turns 

insignificant after 1984. But unlike the employment case, the response of hours to 

current predicted shocks is insignificant for the pre-1984 period and turns negative and 

significant for the post-1984 sample.18 A negative response can happen if much of the 

work-hour adjustment in response to current predicted shocks takes place just prior to the 

month of the shock. As for future predicted shocks, the coefficient becomes smaller 

during the second period, and the difference between the two is statistically significant. 

 For inventories, the coefficients are not statistically significant for either current 

demand shock for either period.19 However, for future predicted shocks, the coefficient is 

negative and significant at the 1% level prior to 1984 and turns positive and insignificant 

after 1984. It is puzzling that inventory is relatively insensitive to current demand and 

responds negatively to future demand for the pre-1984 sample.20 In general, we do not 

 

18 An upper limit on work hours or disutility of working overtime may create a smoothing incentive in 

response to current predicted shocks. 

19 This does not indicate that the model is inappropriate for capturing inventory responses to demand 

shocks. For example, when the same exercise is done using Japanese manufacturing data, we obtain 

significant coefficients with expected signs. The size of coefficients is also much larger. These results can 

be made available upon request. 

20 Since inventory stocks are valued at historical prices, deflating by PPI may lead to some measurement 

error depending upon the age composition of inventories. An attempt was made to overcome this problem 

by using seasonally adjusted real manufacturing monthly inventory data since 1967 taken from National 

Income and Product Accounts (NIPAs). However, the main results did not change. 
 15

find any observable change in the pattern of inventory adjustment before and after 1984, 

except in its responses to future predicted demand.21

 Tables 2 and 3 show the estimates of the same model when the forecast horizons 

are set at 6 and 12 months, respectively. Overall, the results are similar to the 9-month 

forecast horizon case; the 12-month results in particular are essentially the same. For the 

6-month case, the coefficients on current predicted shocks are insignificant for 

employment and work hours, but their size is similar to the 9-month case. The main 

difference is observed in the inventory adjustment for the 6-month forecast horizon case. 

Table 2 shows that the responses to current demand shocks are all negative and mostly 

significant. However, we still cannot determine if there has been a systematic change in 

inventory responses to current predicted shocks, as the coefficients are not statistically 

different from each other. As for the future predicted shock, the coefficient turns from 

negative to positive as before, but now they are both significant.22 

 Next, in order to examine the sensitivity of the results to the modeling of the 

demand process, I fitted one ARIMA specification for the entire series to model demand 

shocks instead of fitting two separate ARIMA specifications.23 The main results are 

essentially unchanged, as shown in Table 4. The standard error of unpredicted current 

demand shocks falls by 13%, while the elasticity of employment with respect to 

unexpected demand shocks falls by 83% and the elasticity of hours falls by about 64%. 

 

21 In addition, unlike the employment case, note that the coefficients on lagged dependent variables display 

lower persistence for both work hours and inventories. 

22 The change in the coefficient for future predicted shocks suggests that shipment lags were reduced and/or 

firms were able to better prepare for the future increase in demand via inventory management after 1984. 

However, the evidence is still rather weak given that the post-1984 coefficient on future predicted demand 

is insignificant in most cases. 

23 I used AR=4 and MA=3. Due to the lags involved in fitting the model, the sample series covers from 

June 1959 through December 2005. 
 16

 In Table 5, the same exercise was done using seasonally adjusted series in order 

to evaluate the role of seasonality in generating the differences.24 The standard error of 

unpredicted current demand shocks falls by 18% while the employment elasticity to 

current unpredicted shocks drops by 82%. Overall, seasonality seems to play almost no 

role in explaining reduced sensitivity of employment and hours to shocks. Finally, 

although not shown here, the main results were robust to the use of new order series 

instead of shipments to capture demand shocks.25 

 Bai-Perron multiple structural break tests suggest the following structural break 

dates for each equation: September 1983 for the employment equation, January 1982 for 

the work-hour equation, and December 1981 and April 1986 for the inventory equation.26 

The number of structural breaks is chosen by Bayesian information criteria (BIC). 

Although not presented here, dividing the sample series at the suggested structural break 

dates for each equation does not significantly alter the estimates. 

 Reduced responses of employment and work hours raise the possibility of more 

flexible wage responses to shocks after 1984. To investigate this possibility, the same 

regression was run using hourly earnings as a dependent variable while controlling for 

lagged values of all variables used in other regressions. The data on average hourly 

earnings in the manufacturing industry come from BLS’s establishment survey. Nominal 

figures are again deflated using the Producer Price Index (PPI) for finished goods. The 

 

24 The ARIMA specification used for both pre- and post-1984 periods is AR=3 and MA=3. Due to the lags 

involved in fitting the model, the sample series covers from May 1959 through December 2005. 25 Employment and work-hour responses to current unpredicted shocks are slightly smaller for the pre-1984 

sample when using new order series. The results are available upon request. 

26 In contrast, the Andrews-Ploberger structural break test identifies a single break date of each coefficient 

instead of multiple breaks of an entire equation. The following structural break dates are suggested for the 

coefficients on current unpredicted shocks: August 1975 for employment, April 1998 for work hours, and 

May 1996 for inventories. 
 17

results for both seasonally unadjusted and adjusted series are shown in Table 6. In both 

cases, we do not find evidence for a more flexible wage adjustment to aggregate shocks 

after 1984. In particular, the elasticity for current unpredicted shocks has dropped by half 

for both series. However, a more robust test would require a firm-level data set.27 Note 

also that the flexibility of other labor compensation such as bonuses and benefits needs to 

be investigated for a more complete analysis.28 

3. VAR Analysis 

VAR Specifications 

 Vector autoregressions are used to investigate the dynamic responses of 

employment with respect to various aggregate shocks to the economy. Here, the 

aggregate shock measures are the real oil price, the aggregate price level, and the federal 

funds rate. The latter are used to capture monetary policy shocks where the rise in the 

rates corresponds to monetary tightening. 

 In order to recover structural innovations, I use a standard Cholesky 

decomposition by assuming the following order of the contemporaneous correlations 

between structural innovations: real oil price, aggregate price level, fed funds rate, and 

 

27 Davis and Haltiwanger (1990) show that idiosyncratic shocks play a larger role than aggregate or sectorspecific shocks in driving aggregate job flows in the manufacturing industry. Accordingly, it may be 

theoretically possible that wage has become more flexible to idiosyncratic shocks at the firm level and 

exhibits less sensitivity at the aggregate level. Alternatively, it may be possible that wage flexibility for 

individual workers has reduced wage-productivity mismatches that get corrected in response to aggregate 

shocks, thereby reducing wage sensitivity at the aggregate level. Further empirical analysis using a microlevel data set would enable us to formulate a more appropriate theoretical framework. 

28 Average hourly earnings do not capture labor costs entirely as they exclude retroactive payments and 

irregular bonuses, employee benefits (i.e., fringe and medical), and the employer’s share of payroll taxes. 

While the Employment Cost Index (ECI) provides a broader measure of labor cost, the ECI is published 

only quarterly and its total compensation series covers from 1981. The ECI also corrects for the wage 

changes associated with the compositional changes of labor force across occupations and industries. 
 18

employment. I took the first difference of all variables in logs in order to use growth 

rates rather than levels (except the fed funds rates, for which simple difference was 

taken). This ensures stationarity for all variables.29 While the fed funds rates are 

nominal, impulse response functions of employment remain essentially unchanged when 

I use inflation-adjusted real fed funds rates.30

 More formally, let [ ,, , ] Yt = DOIL DP DFUNDS DEMP tt t t , where each variable 

reflects the series discussed above, and represent Yt in linear moving average (MA) form 

in terms of structural innovations [ ,,, ] t ot pt ft et ε εεεε = . That is, 

0 ( ) , (0) Yt t = = BL B B ε . (5) 

B( ) L denotes an infinite-order matrix lag polynomial, and the upper triangular 

components of B0 matrix are zero due to my identification restriction. 

 The real oil price is placed first in the Cholesky decomposition as it is probably 

the most exogenous of the four measures and therefore least likely to be 

contemporaneously affected by various shocks to the economy.31 The aggregate price 

level is placed second as the shock to the real oil price immediately affects the aggregate 

price by construction, while price adjustment should lag in response to other types of 

shocks to the economy if prices are sticky. The fed funds rate is placed before 

employment since, as discussed in Bernanke and Blinder (1992), monetary policy in 

general reacts to economic conditions with some lag due to the time it takes for the 

 

29 Note that impulse response functions of employment remain unchanged when the aggregate price level is 

double differenced or when the fed funds rates are not differenced. 

30 Personal consumption expenditure chain-type price indexes were used to adjust for annual rate of 

inflation. 

31 Granger causality tests for the oil price equation show that other variables (except inflation rate) have 

little power in predicting the movement of the oil price growth rate. 
 19

relevant data to become available. Employment is placed at the end as most economic 

shocks are likely result in some immediate impact on employment. The extent of 

responsiveness should be partly determined by the size of labor adjustment costs. 

 These identification restrictions are probably more appropriate for monthly than 

quarterly series. However, for both monthly and quarterly VARs, impulse response 

functions are largely insensitive to changes in the ordering of variables in the Cholesky 

decomposition. 

Data and Results 

 The VAR exercises use the manufacturing employment series at a monthly 

frequency and aggregate nonfarm employment series at both monthly and quarterly 

frequencies. The employment data are taken from BLS’s establishment survey. The 

monthly oil price series is the price for West Texas Intermediate (domestic spot prices) 

deflated by the PPI.32 As a measure of the aggregate price level, personal consumption 

expenditure chain-type price indexes are used for the monthly VARs and GDP chain-type 

price indexes for the quarterly VARs.33 For other variables, I constructed quarterly series 

by taking an average for each quarter. All series are seasonally adjusted with the 

exception of the federal funds rates. Figures 2 and 3 show, respectively, the series used 

 

32 More specifically, the original series was seasonally adjusted using the X-12 ARIMA process and 

deflated by the seasonally adjusted PPI for all commodities. 

33 Monthly personal consumption expenditure chain-type price indexes come from Personal Income and 

Outlays, and quarterly GDP chain-type price indexes come from GDP Press Release, both provided by the 

Department of Commerce’s Bureau of Economic Analysis (BEA). 
 20

for monthly and quarterly VARs. The series are again split in March 1984 to compare 

the responses before and after that date.34

 Hamilton (1996) argues that oil price changes that are reversed quickly do not 

affect the economy, and that a reduction in oil price does not stimulate the economy to 

the same extent that an increase in oil price stifles the economy. Accordingly, I ran 

VARs using the Hamilton oil price measure, which considers only major positive price 

changes relevant to the economy.35 Although these results are not presented, the main 

results did not change. 

 Figures 4 and 5 show, respectively, the impulse response functions of monthly 

manufacturing employment before and after March 1984 with respect to one unit increase 

in each structural innovation (i.e., orthogonalized innovation). The variances of 

structural innovations are normalized to one. The number of lags for VARs was set equal 

to 12 to cover the entire year.36 The dotted lines show the error bands equivalent to a 

two-standard-deviation confidence interval, constructed using Monte Carlo integration as 

suggested by Sims and Zha (1999). The figures indicate that dynamic employment 

responses to each structural innovation and the corresponding error bands are, in general, 

larger before 1984, suggesting that there was much greater uncertainty in terms of 

forecasting employment responses to each of these shocks. 

 

34 Although the real oil price remained rather steady prior to the first oil shock, excluding the period before 

1973 does not change the main results. Also, note that the volatility of real oil price growth is higher after 

1984 even though extremely large spikes such as the one observed in 1973 are absent. 

35 The measure takes the higher of (i) zero and (ii) the difference between the real oil price for month t and 

the maximum real oil price during the preceding 12 months. This filters out the price changes that offset 

each other within a year. 

36 First the optimal number of lags was chosen based on the Akaike information criterion for the number of 

lags between 1 and 20 for the entire sample period. When this number was less than the number to cover 

the entire year (i.e., 12 for the monthly VARs), the latter was used. 
 21

 Figure 6 shows the same impulse response functions displayed in the previous 

two figures, but I put pre- and post-1984 impulse response functions together to facilitate 

the comparison for each shock. The solid line shows the pre-1984 impulse response 

functions, and the dashed line shows those for the post-1984 period. Figure 6 shows that 

the oil price shock negatively affects the employment growth rate and raises volatility 

before 1984, while the response is much milder after 1984. Similarly, the aggregate price 

shock leads to higher volatility in monthly employment growth prior to 1984. 

Furthermore, the monetary shock causes an initial rise followed by a longer period of 

negative growth in employment before 1984, while it does not seem to affect the 

employment growth rate significantly after 1984.37 

 Employment growth responses to a unit shock to the structural innovation of 

employment equation do not provide much of a meaningful interpretation. Since the 

variances of structural innovations are normalized to one, the first period response in the 

impulse response functions is the standard error of the reduced form innovations. 

 I also implemented the same VARs using annual growth rates instead of monthto-month growth rates.38 The number of lags is set equal to 15 based on the Akaike 

information criterion. Figure 7 shows the results. Here again we observe higher 

volatility in the responses of manufacturing employment growth rates to each of the 

structural shocks. One notable feature is that the impact of an oil price shock has a more 

persistent negative impact on employment after 1984. 

 

37 The initial positive spike in employment for the pre-1984 VAR is unobserved if we place employment 

series before the fed funds rates in Cholesky decomposition. 

38 Again, for the fed funds rate, a simple difference over a year is taken instead of the log difference. 
 22

 Figures 8 and 9 show the impulse response functions of monthly aggregate 

nonfarm employment growth rates before and after March 1984, with respect to one unit 

increase in each structural innovation.39 The main results are similar to the analysis of 

manufacturing industry: employment responses are more pronounced and error bands are 

bigger for the pre-1984 sample. Figure 10 combines the two periods to facilitate the 

comparison. Again, the solid line corresponds to pre-1984 impulse response functions 

and the dashed line corresponds to post-1984 functions. Figure 11 uses an annual growth 

rate instead of a one-month growth rate.40 In both cases, the aggregate employment 

responses to each of the shocks are similar to the manufacturing case. 

 Figure 12 shows the impulse response functions of aggregate employment growth 

rates at a quarterly frequency.41 All variables except aggregate price are averaged across 

months for each quarter. Quarterly series on a GDP deflator were used to construct a 

quarterly inflation measure. Obviously, quarterly impulse response functions exhibit 

smoother responses than monthly ones due to time aggregation. By and large, the results 

for aggregate quarterly series confirm the results obtained from the monthly aggregate 

series. Figure 13 uses an annual instead of a quarterly growth rate.42 The main 

difference compared to the monthly case given by Figure 11 seems to be that the 

volatility of employment growth does not fall as much after 1984 in response to oil price 

and aggregate price shocks. 

 

39 Again, the selected number of lags is 12 for both periods. 

40 The number of lags is set equal to 15 based on the Akaike information criterion (AIC). 

41 The number of lags equals 5 based on AIC. 

42 The number of lags equals 6 based on AIC. 
 23

 Figures 14 and 15, respectively, show the same monthly and quarterly VARs 

using the real average hourly earnings growth rate instead of aggregate employment 

growth rate.43 For the monthly VARs, real hourly earnings growth is almost equally 

responsive to each of the shocks. For the quarterly VARs, it is equally or more 

responsive before 1984. Again, these exercises do not find evidence of an increased 

flexibility in aggregate hourly earnings. However, as mentioned previously, a more 

robust test would require a firm-level analysis and an examination of the flexibility in 

other compensation such as benefits.44

 Tables 7 and 8 show, respectively, the results of variance decomposition for the 

monthly manufacturing and aggregate employment series. For the manufacturing case, 

the fraction of the forecast variance explained by the two price measures declined while 

that of the fed funds rate remained more or less the same after 1984. Aggregate 

employment, however, exhibits an opposite pattern. Although it is not clear what 

explains the difference, the increase in the influence of sector-specific shocks affecting 

manufacturing employment may partially account for it. Note that in both cases, the oil 

price, the aggregate price level, and the fed funds rate play a small role in explaining 

overall employment forecast variance. Consequently, a large fraction of the disturbances 

driving employment series fluctuations remains to be identified.45 

 

43 The data on real average hourly earnings for the total private sector are from BLS’s establishment survey. 

44 The Employment Cost Index (ECI) was preferred, but was not used for the quarterly VARs due to its 

short coverage before 1984. 

45 An instrument for demand shocks may be needed to better explain the overall dynamics of employment 

growth rates. Demand shocks were not used for the VARs as the identification requires us to impose more 

structure. This topic will be left for future research. 
 24

 Stock and Watson (2002) find that shocks, not the propagation mechanism, drive 

the dynamics of the four-quarter GDP growth rate volatility. In order to evaluate the role 

of the post-1984 error structure in reducing volatility, the estimated lag coefficients from 

the pre-1984 period and the post-1984 error covariance matrix of reduced form 

innovations were used to forecast the post-1984 sample standard deviations. Likewise, to 

evaluate the relative importance of the post-1984 propagation mechanism in reducing the 

volatility, the pre-1984 error covariance matrix of reduced form innovations and the post1984 lag coefficients were used to estimate the post-1984 sample standard deviations. 

 The results are shown in Table 9.46 The last two columns of the table show the 

hypothetical standard deviations of the variables implied by the above-mentioned 

combinations of lag coefficients and error covariance matrices of the reduced form 

innovations. The table shows that imposing the post-1984 reduced form error covariance 

structure explains much of the variation in employment series—74% of the reduction for 

monthly manufacturing employment series and 85% for monthly aggregate employment 

series. At the same time, imposing the post-1984 coefficients fails to reduce the implied 

standard deviation of employment. In other words, the results are consistent with Stock 

and Watson (2002) as the changes in the lag coefficients play a small role in explaining 

the reduced volatility.47

 Even though these exercises may lead one to conclude that shocks are more 

important than the propagation mechanism, I caution against dismissing the structural 

change argument. As variance decomposition tables show, the oil price, the aggregate 

 

46 Note that the sample standard deviation of real oil price growth rate is higher in the post-1984 period 

since oil prices were very stable between 1958 and 1973. 

47 I thank Stock and Watson for providing the RATS code on their website. 
 25

price level, and the fed funds rate play relatively small roles in explaining the overall 

variation of employment: the larger part is attributed to unidentified shocks. 

Accordingly, the decrease in shocks may appear to be more important than the reduced 

responses to the oil price and the fed funds rate. However, one must be cautious in 

interpreting this result as smaller unidentified shocks may actually be the manifestation of 

favorable structural changes.48 While the model is far from complete, investigation of 

employment responses to these shocks should elucidate the hypothesis as to how 

employment may respond to other unidentified shocks. 

4. Conclusion 

 The U.S. economy has demonstrated a substantial decline in volatility since the 

mid-1980s. An interesting question is whether changes in the shock processes are 

entirely responsible for the increased stability, or whether structural changes that 

increased the resilience of the economy to shocks are partly responsible for the increased 

stability. To investigate this question, this paper analyzed employment responses to 

various shocks to the economy and found that these responses have been smaller since 

the mid-1980s than from the 1960s through the mid-1980s. The results suggest that some 

structural changes may have been partly responsible for the increased stability. 

 Using Topel’s interrelated factor demand model, this paper finds that the monthly 

employment elasticity to unpredicted demand shocks has decreased by more than 80% in 

the manufacturing industry. Similarly, work-hour elasticity to unpredicted demand 

 

48 For example, a better financial environment that leads to smaller adverse effects from financial shocks 

could show up as smaller employment shocks. I owe this point to Ufuk Demiroglu. 
 26

shocks fell by more than 60%. Employment responses to current predicted demand 

shocks also declined but by a smaller amount, perhaps due to a smoothing effect. Both 

employment and work-hour responsiveness to future predicted demand fell. Inventory 

responses to current demand shocks are insignificant in most cases, and even when 

significant, the coefficients are not significantly different from each other. For future 

demand, the inventory coefficient turns from negative to positive, but only the negative 

ones are significant. Overall, the paper does not find any observable change in inventory 

adjustment after 1984, except in its responses to future predicted demand. 

 VARs were used to investigate the dynamic employment responses to aggregate 

shocks for the manufacturing series at monthly frequency and for the aggregate series at 

monthly and quarterly frequencies. Impulse response functions show that both the size 

and volatility of dynamic employment growth responses to the oil price, the aggregate 

price level, and monetary policy shocks have decreased since the mid-1980s, but variance 

decomposition exercises reveal that the role of these shocks in explaining the forecasting 

variance is small. An instrument for demand shocks may be needed to better explain the 

overall dynamics. 

 Finally, an interesting question involves the theoretical underpinnings of the 

reduced employment sensitivity to shocks. One possibility is that wage flexibility has led 

to reduced employment volatility. Although simple exercises done in this paper do not 

find evidence of increased flexibility in aggregate hourly earnings, a more robust analysis 

would require a micro analysis using a firm-level data set with an examination of total 

compensation flexibility including benefits. Alternatively, flexibility within firms may 
 27

have increased at other margins of adjustment. For instance, a model with financial 

innovations that give firms more financial flexibility may explain the observed results. It 

is also possible that nonconvex labor adjustment costs generate a disproportional 

reduction in employment sensitivity when the size of shocks is smaller. Further 

theoretical and empirical research in this area would help us better understand the 

stability of the U.S. economy. 
 28

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 Macroeconomic Stability: Good Luck, Good Policies, or Good Practices?” 

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 and Consequences,” in Mark Gertler and Kenneth Rogoff, eds., NBER

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Davis, Steven J. and John Haltiwanger (1990), “Gross Job Creation and Destruction: 

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 Responses to Oil Price Changes,” NBER Working Paper, No. 7095. 
 29

Davis, Steven J., John Haltiwanger, Ron Jarmin, and Javier Miranda (2006), “Volatility 

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Hamilton, James (1996), “This is What Happened to the Oil Price-Macroeconomic 

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Herrera, Ana Maria and Elena Pesavento (2005), “The Decline in U.S. Output Volatility: 

Structural Changes in Inventory Investment,” Journal of Business and Economic 

Statistics, Vol. 23, No. 4, pp. 462-472. 

Jermann, Urban and Vincenzo Quadrini (2006), “Financial Innovations and 

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 United States: What Has Changed Since the Early 1980s,” American Economic 

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Econometrica, Vol. 65, No. 5, pp. 1113-1155. 
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 31

Figures and Tables 

Figure 1: Manufacturing Monthly Shipments, Employment, Work Hours, and Inventories 

(in logs) from January 1958 to December 2005 

Real Shipments

1959 1966 1973 1980 1987 1994 2001

6.5

7.0

7.5

8.0

Employment

1959 1966 1973 1980 1987 1994 2001

9.54

9.63

9.72

9.81

9.90

Hours

1959 1966 1973 1980 1987 1994 2001

3.60

3.64

3.68

3.72

3.76

Real Inventory

1959 1966 1973 1980 1987 1994 2001

6.00

6.25

6.50

6.75

7.00

7.25

Figure 2: Monthly Series Used for VARs from February 1959 to September 2005 

DOIL

1960 1967 1974 1981 1988 1995 2002

-45

0

45

90

DEMP

1960 1967 1974 1981 1988 1995 2002

-1.0

-0.5

0.0

0.5

1.0

1.5

DP

1960 1967 1974 1981 1988 1995 2002

-0.3

0.0

0.3

0.6

0.9

1.2

DEMPM

1960 1967 1974 1981 1988 1995 2002

-3

-2

-1

0

1

2

DFUNDS

1960 1967 1974 1981 1988 1995 2002

-7.2

-5.4

-3.6

-1.8

-0.0

1.8

3.6

DHW

1960 1967 1974 1981 1988 1995 2002

-1.8

-1.2

-0.6

0.0

0.6

1.2

1.8

Note: Real oil price growth rate (DOIL), inflation rate (DP), change in the fed funds rates (DFUNDS), total 

nonfarm employment growth rate (DEMP), manufacturing employment growth rate (DEMPM), and total 

private real hourly earnings growth rate (DHW). 
 32

Figure 3: Quarterly Series Used for VARs from 1954:Q4 to 2005:Q3 

DOIL

1955 1962 1969 1976 1983 1990 1997 2004

-75

-50

-25

0

25

50

75

DEMP

1955 1962 1969 1976 1983 1990 1997 2004

-1.8

-1.2

-0.6

0.0

0.6

1.2

1.8

DP

1955 1962 1969 1976 1983 1990 1997 2004

0.0

0.8

1.6

2.4

3.2

DHW

1955 1962 1969 1976 1983 1990 1997 2004

-2.4

-1.6

-0.8

-0.0

0.8

1.6

2.4

DFUNDS

1955 1962 1969 1976 1983 1990 1997 2004

-4

-2

0

2

4

6

8

Note: Real oil price growth rate (DOIL), inflation rate (DP), change in the fed funds rates (DFUNDS), total 

nonfarm employment growth rate (DEMP), and real hourly earnings growth rate (DHW). 
 33

Figure 4: Impulse Response Functions of Manufacturing Employment, Monthly Series from 

February 1960 to March 1984 S hoc k to

DOIL

0 5 10 15 20 25 30 35

-0.2

-0.1

0.0

0.1

0.2

0.3

DP

0 5 10 15 20 25 30 35

-0.2

-0.1

0.0

0.1

0.2

0.3

DFUNDS

0 5 10 15 20 25 30 35

-0.2

-0.1

0.0

0.1

0.2

0.3

DEMP

0 5 10 15 20 25 30 35

-0.2

-0.1

0.0

0.1

0.2

0.3

Figure 5: Impulse Response Functions of Manufacturing Employment, Monthly Series from 

April 1984 to September 2005 S hoc k to

DOIL

0 5 10 15 20 25 30 35

-0.2

-0.1

0.0

0.1

0.2

0.3

DP

0 5 10 15 20 25 30 35

-0.2

-0.1

0.0

0.1

0.2

0.3

DFUNDS

0 5 10 15 20 25 30 35

-0.2

-0.1

0.0

0.1

0.2

0.3

DEMP

0 5 10 15 20 25 30 35

-0.2

-0.1

0.0

0.1

0.2

0.3
 34

Figure 6: Impulse Response Functions of Manufacturing Employment, Monthly Series S hoc k to

1960:2-1984:3 1984:4-2005:9

DOIL

0 5 10 15 20 25 30 35

-0.12

-0.09

-0.06

-0.03

0.00

0.03

1960:2-1984:3 1984:4-2005:9

DP

0 5 10 15 20 25 30 35

-0.050

-0.025

0.000

0.025

0.050

1960:2-1984:3 1984:4-2005:9

DFUNDS

0 5 10 15 20 25 30 35

-0.06

-0.03

0.00

0.03

0.06

0.09

1960:2-1984:3 1984:4-2005:9

DEMP

0 5 10 15 20 25 30 35

-0.09

0.00

0.09

0.18

0.27

0.36

0.45

Figure 7: Impulse Response Functions of Manufacturing Employment, 12-Month Growth S hoc k to

1961:4-1984:3 1984:4-2005:9

DOIL

0 5 10 15 20 25 30 35

-0.4

-0.2

0.0

0.2

0.4

1961:4-1984:3 1984:4-2005:9

DP

0 5 10 15 20 25 30 35

-0.75

-0.50

-0.25

0.00

0.25

1961:4-1984:3 1984:4-2005:9

DFUNDS

0 5 10 15 20 25 30 35

-0.75

-0.50

-0.25

0.00

0.25

1961:4-1984:3 1984:4-2005:9

DEMP

0 5 10 15 20 25 30 35

-0.35

0.00

0.35

0.70
 35

Figure 8: Impulse Response Functions of Aggregate Employment, Monthly Series from 

February 1960 to March 1984 S hoc k to

DOIL

0 5 10 15 20 25 30 35

-0.10

-0.05

0.00

0.05

0.10

DP

0 5 10 15 20 25 30 35

-0.10

-0.05

0.00

0.05

0.10

DFUNDS

0 5 10 15 20 25 30 35

-0.10

-0.05

0.00

0.05

0.10

DEMP

0 5 10 15 20 25 30 35

-0.10

-0.05

0.00

0.05

0.10

Figure 9: Impulse Response Functions of Aggregate Employment, Monthly Series from 

April 1984 to September 2005 S hoc k to

DOIL

0 5 10 15 20 25 30 35

-0.10

-0.05

0.00

0.05

0.10

DP

0 5 10 15 20 25 30 35

-0.10

-0.05

0.00

0.05

0.10

DFUNDS

0 5 10 15 20 25 30 35

-0.10

-0.05

0.00

0.05

0.10

DEMP

0 5 10 15 20 25 30 35

-0.10

-0.05

0.00

0.05

0.10
 36

Figure 10: Impulse Response Functions of Aggregate Employment, Monthly Series S hoc k to

1960:2-1984:3 1984:4-2005:9

DOIL

0 5 10 15 20 25 30 35

-0.05

-0.04

-0.03

-0.02

-0.01

0.00

0.01

1960:2-1984:3 1984:4-2005:9

DP

0 5 10 15 20 25 30 35

-0.024

-0.012

0.000

0.012

0.024

1960:2-1984:3 1984:4-2005:9

DFUNDS

0 5 10 15 20 25 30 35

-0.028

-0.014

0.000

0.014

0.028

1960:2-1984:3 1984:4-2005:9

DEMP

0 5 10 15 20 25 30 35

-0.05

0.00

0.05

0.10

0.15

0.20

Figure 11: Impulse Response Functions of Aggregate Employment, 12-Month Growth S hoc k to

1961:4-1984:3 1984:4-2005:9

DOIL

0 5 10 15 20 25 30 35

-0.2

-0.1

0.0

0.1

0.2

1961:4-1984:3 1984:4-2005:9

DP

0 5 10 15 20 25 30 35

-0.28

-0.14

0.00

0.14

1961:4-1984:3 1984:4-2005:9

DFUNDS

0 5 10 15 20 25 30 35

-0.36

-0.27

-0.18

-0.09

-0.00

0.09

1961:4-1984:3 1984:4-2005:9

DEMP

0 5 10 15 20 25 30 35

-0.2

-0.1

0.0

0.1

0.2

0.3
 37

Figure 12: Impulse Response Functions of Aggregate Employment, Quarterly Series S hoc k to

1956:Q1-84:Q1 1984:Q2-2005:Q3

DOIL

0 5 10 15 20

-0.14

-0.07

0.00

0.07

1956:Q1-84:Q1 1984:Q2-2005:Q3

DP

0 5 10 15 20

-0.15

-0.10

-0.05

0.00

0.05

0.10

1956:Q1-84:Q1 1984:Q2-2005:Q3

DFUNDS

0 5 10 15 20

-0.14

-0.07

0.00

0.07

0.14

1956:Q1-84:Q1 1984:Q2-2005:Q3

DEMP

0 5 10 15 20

-0.1

0.0

0.1

0.2

0.3

0.4

Figure 13: Impulse Response Functions of Aggregate Employment, 4-Quarter Growth S hoc k to

1957:Q1-84:Q1 1984:Q2-2005:Q3

DOIL

0 5 10 15 20

-0.32

-0.16

0.00

0.16

0.32

1957:Q1-84:Q1 1984:Q2-2005:Q3

DP

0 5 10 15 20

-0.28

-0.14

0.00

0.14

0.28

1957:Q1-84:Q1 1984:Q2-2005:Q3

DFUNDS

0 5 10 15 20

-0.70

-0.35

0.00

0.35

1957:Q1-84:Q1 1984:Q2-2005:Q3

DEMP

0 5 10 15 20

-0.2

0.0

0.2

0.4

0.6

0.8
 38

Figure 14: Impulse Response Functions of Real Hourly Earnings, Monthly Series S hoc k to

1965:2-1984:3 1984:4-2005:9

DOIL

0 5 10 15 20 25 30 35

-0.100

-0.075

-0.050

-0.025

-0.000

0.025

1965:2-1984:3 1984:4-2005:9

DP

0 5 10 15 20 25 30 35

-0.12

-0.09

-0.06

-0.03

0.00

0.03

0.06

1965:2-1984:3 1984:4-2005:9

DFUNDS

0 5 10 15 20 25 30 35

-0.06

-0.03

0.00

0.03

1965:2-1984:3 1984:4-2005:9

DWAGE

0 5 10 15 20 25 30 35

-0.1

0.0

0.1

0.2

0.3

Figure 15: Impulse Response Functions of Real Hourly Earnings, Quarterly Series S hoc k to

1965:Q2-84:Q1 1984:Q2-2005:Q3

DOIL

0 5 10 15 20

-0.180

-0.135

-0.090

-0.045

-0.000

0.045

1965:Q2-84:Q1 1984:Q2-2005:Q3

DP

0 5 10 15 20

-0.25

-0.20

-0.15

-0.10

-0.05

-0.00

0.05

1965:Q2-84:Q1 1984:Q2-2005:Q3

DFUNDS

0 5 10 15 20

-0.27

-0.18

-0.09

-0.00

0.09

1965:Q2-84:Q1 1984:Q2-2005:Q3

DWAGE

0 5 10 15 20

-0.18

0.00

0.18

0.36

0.54
 39

Table 1: Estimates of Interrelated Factor Demand Model Using Seasonally Unadjusted 

Series and Separate ARIMA Models, 9-month forecast horizon, 1959-2005 

 (1) (2) (3) 

 Employment Hours Inventories 

 Pre-1984 Post-1984 Pre-1984 Post-1984 Pre-1984 Post-1984 

Demand: 

 Current unpredicted 0.096*** 0.011 0.094*** 0.032 0.002 -0.015

 (0.018) (0.009) (0.032) (0.029) (0.050) (0.037)

 Current predicted 0.037*** -0.009 0.025 -0.040* -0.030 0.034

 (0.013) (0.009) (0.017) (0.024) (0.033) (0.033)

 Future predicted 0.104*** 0.027*** 0.079*** 0.043*** -0.094*** 0.037

 (0.012) (0.007) (0.015) (0.015) (0.030) (0.023)

Lagged Dep. Variables: 

 Employment 0.844*** 0.983*** -0.060** 0.084*** 0.127** 0.078*

(0.020) (0.013) (0.024) (0.029) (0.051) (0.046)

 Hours 0.051 0.044* 0.712*** 0.627*** 0.140 -0.136*

(0.033) (0.021) (0.043) (0.053) (0.086) (0.077)

 Inventories -0.056*** -0.044*** -0.027** -0.057** 0.992*** 0.862***

 (0.011) (0.008) (0.013) (0.017) (0.029) (0.027)

Other Lagged Variables: 

 Material and supply -0.043*** 0.019** -0.035*** -0.012 0.027 0.051

 inventories (0.008) (0.09) (0.009) (0.021) (0.020) (0.033)

 Work-in-progress 0.048*** -0.004 0.021* -0.015* -0.017 -0.033***

 inventories (0.010) (0.004) (0.012) (0.008) (0.026) (0.013)

 

Number of obs. 289 252 289 252 289 252

R-squared 0.997 0.999 0.835 0.847 0.996 0.992

Breusch-Godfrey Test 0.839 0.766 0.096 0.245 0.853 0.820

Note: I impose an Almon-type restriction that the distribution of the coefficients on the predicted future 

shipments is assumed to be polynomial of the third degree. Therefore, the shortest possible period of 

prediction is 4 months. Here, the coefficient on future predicted shipments is the sum of the coefficients on 

the 9-month forecast, including the current month. Each regression includes seasonal dummies and a trend 

variable. Beach and MacKinnon maximum likelihood iterative procedure was used to obtain consistent 

estimates in the presence of autocorrelated disturbances. The Breusch-Godfrey Test shows the significance 

level of the test statistic for autocorrelation based on χ2

 distribution. The standard errors are reported in 

parentheses. *, **, and *** show the significance level at 10%, 5%, and 1%, respectively. 
 40

Table 2: Estimates of Interrelated Factor Demand Model Using Seasonally Unadjusted 

Series and Separate ARIMA Models, 6-month forecast horizon, 1959-2005 

 (1) (2) (3) 

 Employment Hours Inventories 

 Pre-1984 Post-1984 Pre-1984 Post-1984 Pre-1984 Post-1984 

Demand: 

 Current unpredicted 0.089*** 0.011 0.115*** 0.022 -0.097 -0.090**

 (0.022) (0.010) (0.041) (0.033) (0.061) (0.038)

 Current predicted 0.025 -0.010 0.044 -0.055 -0.139*** -0.094**

 (0.019) (0.011) (0.030) (0.033) (0.051) (0.041)

 Future predicted 0.102*** 0.029*** 0.081*** 0.040*** -0.104*** 0.045*

 (0.012) (0.006) (0.015) (0.014) (0.030) (0.023)

Lagged Dep. Variables: 

 Employment 0.852*** 0.981*** -0.071*** 0.088*** 0.134*** 0.077*

 (0.018) (0.013) (0.023) (0.028) (0.048) (0.045)

 Hours 0.046 0.042 0.723*** 0.639*** 0.164* -0.173***

 (0.032) (0.020) (0.042) (0.052) (0.084) (0.074)

 Inventories -0.057*** -0.042*** -0.028** -0.053*** 0.991*** 0.873***

 (0.011) (0.008) (0.013) (0.017) (0.029) (0.027)

Other Lagged Variables: 

 Material and supply -0.041*** 0.018* -0.037*** -0.016 0.027 0.043

 inventories (0.007) (0.009) (0.009) (0.020) (0.019) (0.033)

 Work-in-progress 0.046*** -0.004 0.023** -0.014* -0.015 -0.030**

 inventories (0.010) (0.004) (0.012) (0.007) (0.025) (0.013)

 

Number of obs. 292 255 292 255 292 255

R-squared 0.997 0.999 0.834 0.848 0.996 0.992

Breusch-Godfrey Test 0.880 0.788 0.084 0.248 0.865 0.904

Note: The coefficient on future predicted shipments is the sum of the coefficients on the 6-month forecast, 

including the current month. The standard errors are reported in parentheses. *, **, and *** show the 

significance level at 10%, 5%, and 1%, respectively. 
 41

Table 3: Estimates of Interrelated Factor Demand Model Using Seasonally Unadjusted 

Series and Separate ARIMA Models, 12-month forecast horizon, 1959-2005

 (1) (2) (3) 

 Employment Hours Inventories 

 Pre-1984 Post-1984 Pre-1984 Post-1984 Pre-1984 Post-1984 

Demand: 

 Current unpredicted 0.097*** 0.018* 0.096*** -0.017 -0.010 -0.004

 (0.017) (0.009) (0.029) (0.028) (0.047) (0.036)

 Current predicted 0.035*** -0.002 0.028** -0.037** -0.039 0.042*

 (0.010) (0.007) (0.012) (0.017) (0.026) (0.025)

 Future predicted 0.104*** 0.026*** 0.080*** 0.055*** -0.096*** 0.026

 (0.011) (0.007) (0.014) (0.015) (0.030) (0.024)

Lagged Dep. Variables: 

 Employment 0.848*** 0.987*** -0.051** 0.075** 0.115** 0.085*

(0.020) (0.013) (0.024) (0.029) (0.053) (0.046)

 Hours 0.050 0.045** 0.699*** 0.610*** 0.156* -0.096

(0.034) (0.021) (0.044) (0.053) (0.089) (0.077)

 Inventories -0.061*** -0.045*** -0.027* -0.055*** 1.002*** 0.870***

 (0.012) (0.008) (0.014) (0.017) (0.031) (0.027)

Other Lagged Variables: 

 Material and supply -0.044*** 0.017* -0.035*** -0.014 0.029 0.046

 inventories (0.008) (0.009) (0.009) (0.020) (0.020) (0.033)

 Work-in-progress 0.049*** -0.005 0.018 -0.012 -0.019 -0.033*

 inventories (0.010) (0.004) (0.012) (0.008) (0.026) (0.012)

 

Number of obs. 286 249 286 249 286 249

R-squared 0.997 0.999 0.838 0.853 0.996 0.992

Breusch-Godfrey Test 0.827 0.762 0.109 0.234 0.829 0.853

Note: The coefficient on future predicted shipments is the sum of the coefficients on the 12-month forecast, 

including the current month. The standard errors are reported in parentheses. *, **, and *** show the 

significance level at 10%, 5%, and 1%, respectively. 
 42

Table 4: Estimates of Interrelated Factor Demand Model Using Seasonally Unadjusted 

Series and Same ARIMA Model, 9-month forecast horizon, 1959-2005

 (1) (2) (3) 

 Employment Hours Inventories 

 Pre-1984 Post-1984 Pre-1984 Post-1984 Pre-1984 Post-1984 

Demand: 

 Current unpredicted 0.092*** 0.016* 0.095*** 0.034 0.008 0.023

 (0.018) (0.009) (0.030) (0.029) (0.049) (0.034)

 Current predicted 0.032** -0.003 0.026 -0.032 -0.025 0.038

 (0.013) (0.008) (0.017) (0.021) (0.034) (0.030)

 Future predicted 0.101*** 0.026*** 0.072*** 0.047*** -0.097*** 0.024

 (0.012) (0.007) (0.015) (0.015) (0.031) (0.024)

Lagged Dep. Variables: 

 Employment 0.848*** 0.981*** -0.070*** 0.079*** 0.130** 0.079*

(0.019) (0.013) (0.023) (0.029) (0.050) (0.046)

 Hours 0.054* 0.051** 0.762*** 0.634*** 0.137* -0.117

(0.030) (0.021) (0.038) (0.054) (0.079) (0.078)

 Inventories -0.057*** -0.044*** -0.028** -0.060*** 0.989*** 0.865***

 (0.011) (0.008) (0.013) (0.018) (0.029) (0.028)

Other Lagged Variables: 

 Material and supply -0.041*** 0.020** -0.035*** -0.012 0.028 0.059*

 inventories (0.008) (0.009) (0.009) (0.021) (0.020) (0.033)

 Work-in-progress 0.047*** -0.004 0.024** -0.014* -0.016 -0.035***

 inventories (0.010) (0.004) (0.012) (0.008) (0.025) (0.013)

 

Number of obs. 298 252 298 252 298 252

R-squared 0.997 0.999 0.833 0.846 0.996 0.992

Breusch-Godfrey Test 0.827 0.690 0.072 0.252 0.887 0.828

Note: The standard errors are reported in parentheses. *, **, and *** show the significance level at 10%, 5%, 

and 1%, respectively. 
 43

Table 5: Estimates of Interrelated Factor Demand Model Using Seasonally Adjusted Series 

and Separate ARIMA Models, 9-month forecast horizon, 1959-2005 

 (1) (2) (3) 

 Employment Hours Inventories 

 Pre-1984 Post-1984 Pre-1984 Post-1984 Pre-1984 Post-1984 

Demand: 

 Current unpredicted 0.093*** 0.018* 0.090*** -0.035 0.004 0.031

 (0.018) (0.010) (0.030) (0.029) (0.050) (0.040)

 Current predicted 0.030** 0.003 0.022 -0.057*** -0.042 0.052

 (0.015) (0.009) (0.018) (0.021) (0.039) (0.035)

 Future predicted 0.104*** 0.034*** 0.071*** 0.065*** -0.095*** 0.011

 (0.011) (0.007) (0.014) (0.015) (0.030) (0.027)

Lagged Dep. Variables: 

 Employment 0.859*** 0.986*** -0.066*** 0.079*** 0.130** 0.062

(0.019) (0.012) (0.022) (0.024) (0.050) (0.044)

 Hours 0.020 0.036 0.764*** 0.633*** 0.129 -0.065

(0.032) (0.024) (0.039) (0.053) (0.085) (0.089)

 Inventories -0.053*** -0.032*** -0.024** -0.026 1.002*** 0.872***

 (0.011) (0.007) (0.012) (0.015) (0.027) (0.027)

Other Lagged Variables: 

 Material and supply -0.043*** 0.006 -0.032*** -0.043** 0.029 0.063*

 inventories (0.007) (0.009) (0.008) (0.018) (0.019) (0.034)

 Work-in-progress 0.042*** -0.004 0.021** -0.008 -0.023 -0.030***

 inventories (0.009) (0.003) (0.011) (0.006) (0.024) (0.012)

 

Number of obs. 290 252 290 252 290 252

R-squared 0.997 0.999 0.839 0.869 0.997 0.994

Breusch-Godfrey Test 0.775 0.674 0.146 0.462 0.924 0.817

Note: The standard errors are reported in parentheses. *, **, and *** show the significance level at 10%, 5%, 

and 1%, respectively. 
 44

Table 6: Estimates of Wage Responses, 9-month forecast horizon, 1959-2005 

 (1) (2) 

Hourly Earnings, 

Unseasonally Adjusted Series 

Hourly Earnings, 

Seasonally Adjusted Series 

 Pre-1984 Post-1984 Pre-1984 Post-1984 

Demand: 

 Current unpredicted 0.084*** 0.047* 0.105*** 0.048

 (0.026) (0.025) (0.025) (0.029)

 Current predicted 0.008 -0.042* 0.012 -0.069***

 (0.018) (0.023) (0.020) (0.026)

 Future predicted 0.056*** 0.008 0.043** 0.019

 (0.020) (0.028) (0.020) (0.027)

Lagged Dep. Variables: 

 Hourly earnings 0.919*** 0.939*** 0.926*** 0.948***

(0.020) (0.031) (0.018) (0.023)

 

Number of obs. 289 252 290 252

R-squared 0.996 0.995 0.997 0.996

Breusch-Godfrey Test 0.724 0.874 0.721 0.889

Note: The coefficient on future predicted shipments is the sum of the coefficients on the 9-

month forecast, including the current month. A separate ARIMA model was used to capture 

the demand shock processes for each period. Other variables included in the regressions are 

lagged value of employment, hours, inventories, material and supply inventories, and workin-progress inventories. The standard errors are reported in parentheses. *, **, and *** 

show the significance level at 10%, 5%, and 1%, respectively. 
 45

Table 7: Variance Decomposition for Monthly Manufacturing Employment 

 % of forecast variance explained by: 

Horizon Oil price Aggregate price Fed funds rate Employment 

1960-1984 

1 0.40 0.37 3.95 95.28 

12 6.66 3.04 6.56 83.74 

24 10.08 7.56 6.18 76.18 

∞ 10.84 8.10 6.09 74.97 

1984-2005 

1 0.35 0.07 1.99 97.59 

12 2.16 2.59 6.42 88.83 

24 2.51 3.67 7.76 86.06 

∞ 2.69 3.68 8.12 85.51 

Table 8: Variance Decomposition for Monthly Aggregate Employment 

 % of forecast variance explained by: 

Horizon Oil price Aggregate price Fed funds rate Employment 

1960-1984 

1 1.00 0.90 1.87 96.23 

12 6.44 3.60 5.90 84.07 

24 8.82 6.84 5.89 78.45 

∞ 8.83 7.52 5.89 77.77 

1984-2005 

1 0.25 0.29 0.54 98.92 

12 6.63 3.19 2.68 87.50 

24 8.77 6.10 2.90 82.22 

∞ 11.21 11.37 3.16 74.26 

Table 9: Implied Standard Deviations from Subsample VARs 

Employment growth rates Standard deviation implied by the VARs 

 1958-1984 1984-2005 

Coef: pre-84 

Error: post-84 

Coef: post-84 

Error: pre-84 

Monthly manufacturing 0.57 0.26 0.34 0.67 

Monthly aggregate 0.27 0.14 0.16 0.28